Pants.pdf research and reflection.

Lab work in 205.

Our species needs, and deserves, a citizenry with minds wide awake and a basic understanding of how the world works. --Carl Sagan What kind of world are we making. What kind of world should we be making. What kind of world can we be making.

Mathematics and Religion (final project ideas: sacred geometry, spiritual numeracy)

Discuss mathematical breakthroughs and revolutions: changing the world.

Math It's Everywhere: https://www.youtube.com/watch?v=gAvIR3vFu8c

Beauty of Mathematics: http://vimeo.com/77330591

Smarter Math Builds Equations for a Smarter Planet

Real-World Problems Being Solved by Mathematicians

Look at the final research presentations and discuss how to research mathematical connections for a number of class interests.

Survey clicker questions

Time to work on the final research presentations

Finish discussing Andrew Wiles and

Why make Liberal Arts Majors take Math in College? https://www.youtube.com/watch?v=bvO1yAzQq9E 3:23

Liberal arts

General Education and Mathematics in a General Education: Liz Colman and Education.

Clicker questions on what is mathematics #7-11

1. Sell your stock (using the original purchase price)

2. Meeting Quantitative Needs

3. You may work on project 4 or the research presentations in the lab or elsewhere (I am happy to help!)

Continue

Share from Project 3 (Critical Analysis of Recent Media)

Share your favorite quote about what mathematics is and the person it is attributed to. Clicker questions on what is mathematics #1-6 and discuss the what mathematics is research and readings hw.

Andrew Wiles and

Come back together in the classroom.

Mathematicians: Jeff Weeks, myself, David Blackwell and Andrew Wiles

Predicting height and solving a crime

1. Can We Predict the Future? Stocks, Class Data, and Raw Egg Regressions

2. If finished before we come back together, then review the class highlights page and take notes for project 4 related to statistics.

Come back together.

Clickers for regression lab

Take questions on test 3 study guide, ASULearn review or anything else.

GE experiment

Discuss correlations versus causations on why birds fly south during colder weather

Discuss the Bradford-Hill criteria

Look at succeeding in mathematics (Circle lots of As):

Case studies: College Success #6

1. Statistics Detective Review

2. Purchase your stock

Collecting and Presenting Data, Boxplots, Predictors, Unintended Consequences:

Clicker questions on the hw readings.

Clicker questions on applications of statistics to our lives hw readings

1. Representations of Data lab

2. Ask me any questions about project 3 before you leave

Clicker questions on elections

2000 election between Bush and Gore and Pat Buchanan's impact in Florida

3.4 #11.

Clicker questions on the hw readings Discuss the hw readings and mention project 3.

Clicker questions on measures of center

Histogram of the ASULearn random number from 1 to 10. experiment and Excel analyses. Discuss whether the human mind can provide a random number. Discuss sampling versus census. Discuss mathematical proof versus statistical significance and randomness. Discuss the expected value (sum/10) and briefly mention the chi test [(B2-C2)^2/C2, CHITEST(B2:B11,C2:C11)] and p-value (are the observations statistically significant or can the differences be ascribed to random variations of chance?)

Discuss Benford's law, where the first digit in many real-life sources of data is not equally distributed, and approximates a logarithmic trend (where 1 occurs about 30% of the time while 9 less than 5% of the time) in data such as street addresses, stock prices, population numbers, death rates, etc...

Distance from home bar chart.

Discuss bar chart of volume of stocks from lab including how you can tell whether the mean will be above or below the median using the idea of a scale balance.

Armspan bar chart.

Height box plots.

In 205:

Finish the statistics of nature.

Mention part of the hw on the articles on the impact of young voters

In 205:

1. ASULearn anonymous data collection.

2. statistics of nature

3. Read through Project 3 and take note of the literature review/connection component as related to the themes of

a) Collecting and Presenting Data

b) Boxplots

c) Predictors

d) Unintended Consequences

So, as you are completing hw for tomorrow, take notes on anything you see related to the above 4 themes

4. Ask me any questions and make sure that I have looked through your lab responses to the statistics of nature before you leave.

Answer questions on the study guide, ASULearn activities and go over the homework.

Review via clickers: 1.2 #9, 14, 21, and 24 and 1.3 # 8 and 10

a) lump sum

b) periodic payment

c) loan payment

d) combination of lump sum and periodic payment

e) other

Discuss local debt. Discuss debt in NC, the US, and the world.

Richard Feynman quotation:

Payday lender in Boone: What is the annual rate?

a) 17.5%

b) 24%

c) 117.5%

d) 455%

e) none of the above

Discuss good credit

Discuss project 4. The people mentioned in the finance segment... Equations in this segment.

Begin statistics: statistics in the geometry segment and in finance

Mention upcoming needed for lab in 2015: Find the stock symbols of a few companies that are actively traded and that you are interested in "buying" - for example, you might search

http://finance.yahoo.com/lookup for stocks with certain names

or www.google.com for

"stock symbol" "COMPANY NAME"

where COMPANY NAME is the name of the company that you are interested in.

stock graph

In 205:

1. Find some stock symbols, as above

2. Stock Graph

Clicker questions on loans

Review the Condo lab questions: 1, 4, 7, 8 and 9-13

a) Option 1

b) Option 2

Second Student loan statement, credit cards and finance charges

In 205:

1. Condo and Car Purchases: Decisions, Decisions (Part 2)

Philosophy of loans Student loan statement.

In 205:

1. Car Loan Practice Problem on ASULearn. Keep track of your calculations on a sheet of paper (if you scroll over an answer box after you submit it, you will receive feedback and hints, and you can resubmit the correct answers online).

2. Condo and Car Purchases: Decisions, Decisions (Part 1)

Clicker questions for lump sum #3-6

What about $100 deposited every month into an account for 25 years, compounded monthly at 5%? Work towards periodic payment understanding and compare the philosophy to the lump sum formula derivation and to Jeff Weeks.

Transparencies from class

Clicker questions for lump and periodic

Begin the lottery questions. Search google news for lottery winner lump.

Picture of Excel work, Excel work file. Picture of Excel solutions, Excel solution file.

In 205:

Jane and Joan on ASULearn. If you are finished early, then ask me any questions you have on Project 2 before you go

Clicker questions for lump sum #1 and 2 Review the lump sum philosophy.

Intro to Goal Seek via using today's rate and seeing how long it will take to double money using her rate of 8% compounded monthly, and then today's rate: =1000*(1+B2/12)^(C2*12)

Goal Seek: Data/What-If Analysis/Goal Seek/Set cell...

Discuss other possibilities for unknowns in lump sum - the amount put in, the rate, or the number of times compounding per year. Lisa's Thrifty Savers savings account from Bart the Fink.

Charlie Rose - An exclusive conversation with Warren Buffett [first 54 seconds and then from 3:30-5:18].[DVD 4:11 - 5:48]

Youtube first 1:27

Quotes on taxation. Local to global taxes.

In 205:

Benjamin Franklin's Will - Part 1 (Lab)

Begin finance.

History and ethics of charging interest for the use of land, animals, money.

Plimpton Cuneiform 322 and interpreting data

Usury is Piracy

Discuss 142 years compounding monthly versus annually.

Lump Sum Philosophy

Real-life bank situation. Past student was told that her c.d. will be compounded monthly at 8% for 8 months, and is told that this 8% will apply each and every month. Let's say that she put in $1000. How much would her c.d. be worth at the end of 8 months?

(a) 1000(1+.08)

(b) 1000(1+.08/8)

(c) 1000(1+.08/12)

(d) 1000(1+.08/12)

(e) none of the above

What did the bank really mean?

Review the lab. Take questions on the quiz, project 4, or the study guide.

1. what mathematics is,

2. what it has to offer and why it is useful,

3. the diverse ways that people succeed in it and impact it,

4. local to global theme,

5. truth and consequenses theme.

Discuss the Jeff Weeks Interview.

visualizing a hypersphere: Jeff Weeks worksheet [Einstein based his theory of relativity off of Riemann's work on this space]

Discuss the local to global theme in this segment.

My own research as a part of the ways that people succeed and impact mathematics

Discuss equations in this segment.

Reflect on equations in the context of "what is mathematics" and the prevalence of equations in and outside of mathematics. Highlight percentages, fractions and decimals.

Google search how many stars in the universe

Dimensions

Shape

Geometry of the Universe slides

Review http://www.youtube.com/watch?v=Uzd484Mvm2k starting at about 4:11, including a 3-torus with only 96 stars

Portal and Futurama: I, Roommate.

Gauss and Lobachevsky's measuring the angle sum

Rob Kirschner's Supernovae results related to whether brightness=1/distance

Discuss the density equation WMAP and Planck launches.

http://www.youtube.com/watch?v=5u7hFQy9Mt0&feature=relate From 47:46 onwards.

Questions or comments on the readings.

In 205:

Universe Lab

Use tape to make an equator. Begin going over the first 4 questions from Project 1

Review http://www.youtube.com/watch?v=Uzd484Mvm2k starting at about 4:11, including a 3-torus with only 96 stars

[~32 minutes] Selections cut from PBS Life by the Numbers: Seeing is Believing Video: Modern artists and mathematicians are trying to grapple with the 4th physical dimension. Mathematics helps define space and helps present visions of our world to us. Tom Banchoff as a mathematician. Shape of the World video: Viewers see how mathematics has become a tool to explore the heavens as the cosmos is charted.

Class concentrates on what our universe looks like, how we know, and how we represent it. Discuss the video, including Tom Banchoff, Rob Kirschner, and Jeff Weeks, Riemann and Einstein, high dimensions, experiments and representations. notes

Discuss and share responses to the notes

Maddie's video

http://www.youtube.com/watch?v=5u7hFQy9Mt0&feature=relate From 47:46 onwards.

Discuss the density equation WMAP and Planck launches.

Portal and Futurama: I, Roommate.

Rob Kirschner's Supernovae results related to whether brightness=1/distance

discuss local (close to Euclidean geometry) to global (geometry is very different) perspectives

Crochet model of hyperbolic geometry There are many real-life applications of hyperbolic geometry, such as

1. models of the internet that hope to reduce the load on routers,

2. building crystal structures to store more hydrogen or absorb more toxic metals

3. mapping the brain

4. mapping the universe

5. modeling Mercury's orbit.

6. Art: Crochet model of hyperbolic geometry Reef Crochet reef.

PacMan sequence from

Discuss what a 2-D creature would see if an orange passed through the plane of existence, including 2-D creature movements of the caterpillar turning into a 3-D movement butterfly

Davide Cervone's Cube Projections.

Introduce the Klein bottle along with the identifications of the square model.

Glass model - I have a much smaller model in my office.

Students create a tiling view of Klein bottle Tic-Tac-Toe to the left and right (same board), and above and below (reflected board).

Watch an excerpt from

In 205:

1. 2-D universe lab

2. If finished before we come back together, then work on project 1.

Prepare to share your name, major(s)/minors/concentrations, and something you learned from hw or class yesterday or had a question on. yesterday's class.

Of the following, what is the most compelling argument (to you) about ways we could know that the earth was round without modern technology?

a) The sun and moon are round so the earth should be (originally attributed to Pythagoras)

b) Ships disappearing on a clear day appear to sink in the horizon

c) Stars change as we change latitude and overlaps flip when we pass over the equator

d) Directions of hurricanes change from Northern to Southern Hemisphere (Coriolis force)

e) On midsummers day at noon, Syene (Aswan) made no shadows, while Alexandria did (Eratosthenes used this to calculate the circumference of the earth)

Lab 1 Clicker questions

What does a space look like, how do we know, and how do we represent it...

Where is North?

Sphere questions:

Experiencing Geometry by Henderson

Geometry Theorems and Constructions by Berele and Goldman

The Heart of Mathematics by Burger and Starbird

Symmetry, Shape and Space by Kinsey and Moore

Universe questions:

Beyond the Third Dimension by Banchoff

Exploring the Shape of Space by Weeks

Geometry, Relativity and the Fourth Dimension by Rucker

The Heart of Mathematics by Burger and Starbird

Hyperspace by Kaku

The Math Book by Pickover

Shape of Space by Weeks

Symmetry, Shape and Space by Kinsey and Moore

3) Are

Dutch graphics artist M.C. Escher and the mathematical clues he left in his work: Sun and Moon (1948) Worksheet on Escher. (number 2). Quotes from Escher on how he does mathematics and where it comes from. Discuss whether mathematics arises from nature or whether we impose our mathematical discoveries onto nature.

First 3 questions on Clicker review of Euclidean and Escher

Escher's space and Poincare's disk model of hyperbolic geometry.

Sphere with Angels and Devils, 1942.

Sphere Surface with Fish. 1958

Discuss a computer model of Escher's space called hyperbolic geometry.

discuss local (close to Euclidean geometry) to global (geometry is very different) perspectives

Watch 10 minute video excerpts lifebynumbersintro.mov notes

Advice from last semester.

Julian Beever's pavement drawings:

Butterfly

Globe wrong view

Globe correct view

Accident

Perspective Drawing and Projective Geometry

Lab work in 205:

1) ASULearn Mathematical Experiences Reflection

2) Perspective lab Activities

3) Are

If time remains before we come back together to review the activities, then work on homework for tomorrow.

What kind of world are we making. What kind of world should we be making. What kind of world can we be making.